Asymmetric semipermeable membranes suitable for use in reverse osmosis processes for producing potable water from brackish or saline water have been known for sometime. Such asymmetric membranes have a thin, dense permselective surface layer supported by a much thicker porous layer of the same polymeric material. Processes for making such asymmetric membranes from cellulose diacetate are disclosed in U.S. Pat. Nos. 3,133,132 and 3,133,137 issued to Loeb et al on May 12, 1964. Since the issuance of the Loeb et al patents, there has been a substantial amount of work done in this area of asymmetric semipermeable membranes, and cellulose diacetate has been one of most intensely investigated polymers for making such membranes. For example, U.S. Pat. No. 3,497,072, issued Feb. 24, 1970 to Cannon, discloses a method for preparing such an asymmetric membrane from cellulose diacetate in a very narrow range of acetyl content. However, these cellulose diacetate membranes are somewhat limited in achieving very high rejection capability and are also vulnerable to hydrolysis when used with aqueous feed solutions having either high or very low pH values. Accordingly, cellulose diacetate membranes have not proved to be economically practical for use in seawater desalinization installations.